Counterexamples in Operator Theory

This text is the first of its kind to exclusively devote to counterexamples in operator theory, featuring over 500 problems on bounded and unbounded linear operators in Hilbert spaces. It is geared towards graduate students studying operator theory and includes difficulty levels for each counterexample. The first half focuses on bounded linear operators, while the second part covers unbounded linear operators. Chapters begin with a "Basics" section and many of the counterexamples are original work.

Format: Paperback / softback
Length: 598 pages
Publication date: 05 May 2023
Publisher: Springer Nature Switzerland AG

This groundbreaking text is the first of its kind, exclusively devoted to counterexamples in operator theory. It encompasses over 500 challenging problems on bounded and unbounded linear operators in Hilbert spaces, making it an invaluable resource for graduate students studying operator theory. The author has carefully designated the difficulty level for each counterexample, indicating which ones are also suitable for advanced undergraduate students.

The book is divided into two parts. The first half focuses on bounded linear operators, delving into various areas such as operator topologies, matrices of bounded operators, square roots, the spectrum, operator exponentials, and non-normal operators. Each chapter begins with a brief "Basics" section, providing valuable reference material for readers. Many of the counterexamples included in this section are the author's original contributions, adding depth and insight to the subject matter.

The second part of the book is dedicated to unbounded linear operators. It explores topics such as closedness and closability, self-adjointness, normality, commutativity, and the spectrum. The chapter concludes with a discussion of open problems, encouraging further research and exploration in this field.

Chapters in this book are well-organized and concise, making it easy to navigate and comprehend the material. They include detailed explanations, examples, and exercises to reinforce the concepts presented. The book is suitable for students in graduate courses on operator theory and advanced matrix theory, as well as researchers, quantum physicists, and undergraduate students studying functional analysis and operator theory.

In conclusion, Counterexamples in Operator Theory is a must-have resource for anyone interested in exploring the boundaries of operator theory. With its comprehensive coverage, challenging problems, and insightful explanations, this book provides a valuable tool for students, researchers, and practitioners in the field.

Weight: 961g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030978167
Edition number: 1st ed. 2022